GATE 2022 MN – Question 51
A battery locomotive pulls mine tubs of total mass 3 tonnes up a 1-in-20 gradient. Rolling-friction coefficient is 0.06 and adhesion coefficient 0.2. It reaches 1.8 m/s from rest in 3 min at constant acceleration. Find minimum locomotive mass in tonnes, to one decimal.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 3.7 to 3.8
Explanation
Acceleration is $1.8/180=0.01$ m/s². Include rolling resistance, gradient resistance and acceleration in $c=0.06+0.05+0.01/9.81=0.111019$. If locomotive mass is M tonnes, required tractive effort is (M+3)gc while adhesion permits 0.2Mg. Equating them gives $M=3c/(0.2-c)=3.74304$ tonnes, or 3.7 tonnes. Both the locomotive and the tubs contribute resistance.